SAT based Bounded Model Checking (BMC) is an efficient method for detecting logical errors in finite-state transition systems. Given a transition system, an LTL property, and a user defined bound k, a bounded model checker generates a propositional formula that is satisfiable if and only if a counterexample to the property of length up to k exists. Standard SAT checkers can be used to check thi...

We prove sharp inequalities for the average number of affine diameters through the points of a convex body K in Rn. These inequalities hold if K is a polytope or of dimension two. An example shows that the proof given in the latter case does not extend to higher dimensions. The example also demonstrates that for n ≥ 3 there exist norms and convex bodies K ⊂ Rn such that the metric projection on...

PURPOSE To describe the cross-sectional relationship between retinal arteriolar and venular diameters with age and blood pressure. METHODS A population-based study was conducted in Beaver Dam, Wisconsin (n=4926, age range, 43-84 years). Retinal photographs of right eyes taken at the baseline examination (1988-90) were digitized. All arterioles and venules located in the area between one-half ...

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA-models. There is a substantial amount of literature proving that, quite generally, PA-graphs posses...

In this paper we consider an on{line problem related to minimizing the diameter of a dynamic tree T. A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree T ffgnfeg. Starting with a tree with n nodes, we show how each such best swap can be found in worst{case O(log 2 n) time. The problem was raised by Italiano and R...